answer:Since y=tanleft( frac {pi}{4}-xright) = -tan(x- frac {pi}{4}), we have x- frac {pi}{4}neq kpi+ frac {pi}{2}, thus xneq kpi+ frac {3}{4}pi, where kinmathbb{Z}. Therefore, the correct choice is boxed{text{D}}. This is derived from the definition of the tangent function, by solving the range of x that does not satisfy the condition. This question examines the definition of the tangent function and belongs to the type of questions that test basic concepts.

answer:We are given a point M(x, y) and need to find the coordinates of this point when reflected over two axes: the x-axis (OX) and the y-axis (OY). **Step 1: Reflection over the x-axis (OX)** 1. Consider the coordinates of the reflected point M' (x', y'). 2. When a point is reflected over the x-axis, its x-coordinate remains the same while the y-coordinate changes sign. Thus, for a point M(x, y): [ x' = x y' = -y ] Therefore, the coordinates of the point M' (reflected over the x-axis) are (x, -y). **Step 2: Reflection over the y-axis (OY)** 1. Again, consider the coordinates of the reflected point M' (x', y'). 2. When a point is reflected over the y-axis, its x-coordinate changes sign while the y-coordinate remains the same. Thus, for a point M(x, y): [ x' = -x y' = y ] Therefore, the coordinates of the point M' (reflected over the y-axis) are (-x, y). # Conclusion After finding the coordinates of the reflected points, we can conclude the following: 1. The coordinates of the point symmetrical to M relative to the x-axis are: [ (x, -y) ] 2. The coordinates of the point symmetrical to M relative to the y-axis are: [ (-x, y) ] Thus, the final answers are: [ boxed{text{a) } (x, -y)} ] [ boxed{text{b) } (-x, y)} ]

answer:1. Dot product of mathbf{a} with itself: [mathbf{a} cdot mathbf{a} = p^2 (mathbf{a} cdot (mathbf{a} times mathbf{b})) + q^2 (mathbf{a} cdot (mathbf{b} times mathbf{c})) + r^2 (mathbf{a} cdot (mathbf{c} times mathbf{a})) + mathbf{a} cdot mathbf{b}.] Since mathbf{a} is orthogonal to both mathbf{a} times mathbf{b} and mathbf{c} times mathbf{a}, and mathbf{a} is orthogonal to mathbf{b}: [mathbf{a} cdot mathbf{a} = q^2 (mathbf{a} cdot (mathbf{b} times mathbf{c})) = 2q^2.] Since mathbf{a} cdot mathbf{a} = 1, we have 2q^2 = 1, leading to q^2 = frac{1}{2}. 2. Dot product of mathbf{a} with mathbf{b}: [0 = p^2 (mathbf{b} cdot (mathbf{a} times mathbf{b})) + q^2 (mathbf{b} cdot (mathbf{b} times mathbf{c}) + r^2 (mathbf{b} cdot (mathbf{c} times mathbf{a}) + mathbf{b} cdot mathbf{a}.] mathbf{a} and mathbf{b} are orthogonal: [0 = r^2 (mathbf{b} cdot (mathbf{c} times mathbf{a})).] Using scalar triple product: [0 = r^2 (2).] So, r^2 = 0. 3. Dot product of mathbf{a} with mathbf{c} gives p^2 = 0 since similar arguments apply. Therefore, p^2 + q^2 + r^2 = 0 + frac{1}{2} + 0 = boxed{frac{1}{2}}.

answer:Solution: From the sequence 3, 5, 9, 17, 33…, we can derive: a_1 = 2^1 - 1, a_2 = 2^2 - 1, a_3 = 2^3 - 1, …, Thus, we can deduce: a_n = 2^n - 1. Therefore, the answer is: 2^n - 1. From the sequence 1, 3, 7, 15, 31, …, we can derive: a_1 = 2^1 - 1, a_2 = 2^2 - 1, a_3 = 2^3 - 1, …, which leads to the conclusion. This question tests the ability to observe, analyze, conjecture, and deduce the general formula of a sequence, emphasizing the application of 2^n, and is considered a basic question. Thus, the general formula for the nth term of this sequence is boxed{2^n - 1}.